Then/Now You named angle pairs formed by parallel lines and transversals. • Use theorems to determine the relationships between specific pairs of angles. • Use algebra to find angle measurements.
Then/Now You named angle pairs formed by parallel lines and transversals. Use theorems to determine the relationships between specific pairs of angles.
Mar 29, 2015
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Then/NowYou named angle pairs formed by parallel lines and transversals.
• Use theorems to determine the relationships between specific pairs of angles.
• Use algebra to find angle measurements.
Concept
Example 1Use Corresponding Angles Postulate
A. In the figure, m11 = 51. Find m15. Tell which postulates (or theorems) you used.
What is the relationship between < 11 and < 15?
15 11 Corresponding Angles Postulate
m15 = m11 Definition of congruent angles
m15 = 51 Substitution
m< 15 = 51
Example 1
Use Corresponding Angles Postulate
B. In the figure, m11 = 51. Find m16. Tell which postulates (or theorems) you used.
16 15 Vertical Angles Theorem
15 11 Corresponding AnglesPostulate
16 11 Transitive Property ()m16 = m11 Definition of congruent
angles
m16 = 51 Substitution
Example 1b
A. 42
B. 84
C. 48
D. 138
B. In the figure, a || b and m18 = 42. Find m25.
Concept
Example 2Use Theorems about Parallel Lines
FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m3.
2 3 Alternate Interior Angles Theorem
m2 = m3 Definition of congruent angles
125 = m3 Substitution
Answer: m3 = 125
Example 2
A. 25
B. 55
C. 70
D. 125
FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m4.
Skills Packet Do #4 - #6
A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.
Example 3Find Values of Variables
5 7 Corresponding Angles Postulate
m5 = m7 Definition of congruent angles
2x – 10 = x + 15 Substitution
x – 10 = 15 Subtract x from each side.
x = 25 Add 10 to each side.
Answer: x = 25
B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y.
Example 3Find Values of Variables
8 6 Corresponding AnglesPostulate
m8 = m6 Definition of congruentangles
4y = m6 Substitution
Example 3Find Values of Variables
m6 + m4 = 180 Supplement Theorem
4y + 4(y – 25) = 180 Substitution
4y + 4y – 100 = 180 Distributive Property
8y = 280 Add 100 to each side.
y = 35 Divide each side by 8.
Answer: y = 35
A. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find x.
Example 3
Skills Packet Do #7 - #11
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